The Orientation Dependence of the Real Part of the Ion–Ion Potential between Two Nuclei

Ismail, M.; Ramadan, Kh. A.; Osman, M. M.; Salah, F.; Ellithi, A. Y.

doi:10.1142/s0217732397002119

Cited by 2 publications

(6 citation statements)

References 17 publications

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“…The behavior of V (R) with the separation distance R and the orientation of the two symmetry axes when existing in the same plane was explained in Refs. [10,11,15,21,26]. Figure 3 shows our results for the 238 potential assuming two coplanar symmetry axes and calculated using Skyrme force with parameter set SIII.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…In almost all the cases it is assumed that the two interacting nuclei have coplanar symmetry axes [10,11,14,16,21] and even θ P = θ T . In the present work we used the Hamiltonian energy density approach derived from the well-known Skyrme interaction to study the orientation dependence of the HI potential between two deformed nuclei.…”

Section: Discussionmentioning

confidence: 99%

“…This method has been applied successfully to derive the real part of the interaction potential between spherical-deformed [19,20] and coplanar deformed-deformed nuclei [21]. The Skyrme interaction is an effective NN force where parameters are chosen to fit the saturation properties of cold nuclear matter and to reproduce static properties such as the total binding energies and charge radii of some nuclei [22,23].…”

Section: Introductionmentioning

confidence: 99%

“…This interaction has been used frequently in nuclear structure calculations and the structure of the super heavy nuclei [24]. The simple form of the Skyrme interaction [25] has considerable advantages in nuclear structure calculations and scattering problems [18][19][20][21]. The main advantage is that its simplicity allows one to write the Hartree-Fock energy as a functional depending only on local densities and their gradients.…”

Section: Introductionmentioning

confidence: 99%

“…The main advantage is that its simplicity allows one to write the Hartree-Fock energy as a functional depending only on local densities and their gradients. The energy density formalism derived from the Skyrme density-dependent interaction has been used to study the orientation dependence of the real part of the ion-ion potential between two coplanar deformed nuclei [21,26]. This approach derived from the conventional Skyrme force [22] together with the extended Skyrme force [27] has been used to study the interaction potential between several systems [28].…”

Section: Introductionmentioning

confidence: 99%

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Orientation dependence of the heavy-ion potential between two deformed nuclei

et al. 2005

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The deformation and orientation dependence of the real part of the interaction potential is studied for two heavy deformed nuclei using the Hamiltonian energy density approach derived from the well-known Skyrme NN interaction with two parameter sets SIII and SkM * . We studied the real part of the heavy ion (HI) potential for 238 U+ 238 U pair considering quadrupole and hexadecapole deformations in both nuclei and taking into consideration all the possible orientations, coplanar and noncoplanar, of the two interacting nuclei. We found strong orientation dependence for the physically significant region of the HI potential. The orientation dependence increases with adding the hexadecapole deformation. The azimuthal angle dependence is found to be strong for some orientations. This shows that taking the two system axes in one plane produces a large error in calculating the physical quantities.

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Section: Numerical Resultsmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Orientation dependence of the heavy-ion potential between two deformed nuclei

et al. 2005

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Azimuthal angle dependence of Coulomb and nuclear interactions between two deformed nuclei

et al. 2007

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The azimuthal angle (φ) variation of the Coulomb and nuclear heavy ion (HI) potentials is studied in the framework of the double folding model, which is derived from realistic nuclear density distributions and a nucleon-nucleon (NN) interaction. The present calculation shows that the variation of HI potentials with the azimuthal angle depends strongly on the range of the NN forces. For the long-range Coulomb force, the maximum variation with φ is about 0.9%, and for HI potential derived from zero-range NN interaction the φ-variation can reach up to 90.0%. Our calculations are compared with the recent φ-dependence of the HI potential derived from proximity method. The present realistic φ-dependence calculations of the HI potential is completely different from the results of the proximity calculations. DOI: 10.1103/PhysRevC.75.064610 PACS number(s): 24.10.−iThe calculations of the nucleus-nucleus potential between two deformed, oriented nuclei have been of much interest [1][2][3][4][5][6][7][8][9]. The double folding model [2,4,10] plays a fundamental role in deriving the heavy ion (HI) potential. For two deformed density distributions, the calculation of the nucleus-nucleus potential is a hard task due to the numerical computation of a six-dimensional integral, which is very time consuming. This problem is quite relevant because most nuclei have permanent and/or vibrational deformations. Recently, many authors have considered this problem to study the synthesis of new and superheavy elements [4,5,7,8], since the collision of deformed nuclei is a path to the far side of the proposed island of superheavy nuclei [11]. For the collision between either two spherical [12], or spherical-deformed nuclei [13], the HI potential (including the Coulomb part) had been derived microscopically by different methods. The double folding model [2,4,10] is one of the successful methods to derive the HI potential starting from a finite range NN force. Moreover, this model is the only one used to treat correctly the Coulomb potential between two heavy ions.For two deformed nuclei, the double folding model can be simplified when their symmetry axes are coplanar [1,2]. For arbitrary orientations of the nuclei, the six-dimensional integral of the double folding model is difficult to calculate without making approximations. Due to this difficulty, many authors considered different approximate methods to derive both the nuclear and Coulomb HI potentials [5][6][7]. For example, in Refs. [6,7] the pocket formula of the proximity potential was used to study orientation dependence of the HI potential. In another study [14], the zero-range NN force was used to reduce the six-dimensional integration to three dimensions. The Coulomb potential, in these recent studies, was calculated from a simplified equation derived by Wong [15], or by assuming the nucleus to be of uniform charge distribution with sharp cutoff edge [5]. The two methods for * ali@mailer.eun.eg calculating the Coulomb potential produce a large error in both internal and surface reg...

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The Orientation Dependence of the Real Part of the Ion–Ion Potential between Two Nuclei

Cited by 2 publications

References 17 publications

Orientation dependence of the heavy-ion potential between two deformed nuclei

Orientation dependence of the heavy-ion potential between two deformed nuclei

Azimuthal angle dependence of Coulomb and nuclear interactions between two deformed nuclei

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